This video, aimed at students aged 16+, opens with Professor Chris Budd holding the plastic yellow duck he is entering in the Annual Bath Plastic Duck Race. Competition is stiff - there are over 3,000 contestants - but how can we predict who will win? Very few competitors have form, and it's hard to tell much about their training regimens... so is the outcome totally unpredictable?

Paul Erdös is reported to have said "A mathematician is a machine for turning coffee into theorems". We may never know if he appreciated the mathematics behind the perfect dunk of a biscuit into said coffee, but we can all begin to understand the ubiquity of maths in our lives, thanks to Len Fisher's delightful book. The subtitle is "The science of everyday life", though pretty much all the content is maths with the equations (mostly) taken out. Perhaps Professor Fisher was advised that sales would suffer if they weren't, but anyone interested in the applications of mathematics to the real world will find plenty to amuse and educate.

One of Oxford University Press's series of "Short Introductions", this book is a rigorous and challenging description, by one of the greatest pure mathematicians alive (Timothy Gowers is Rouse Ball Professor of Mathematics at the University of Cambridge, and a Fields Medal recipient), of what mathematics is. Perhaps too challenging, in fact - on page 23 we are introduced to an axiomatisation of number systems, and things only get tougher. Clearly, as one of a highly intellectual series, the book is intended to stretch its readers' abilities to the utmost.

Since the phenomenal success of "The little book of calm", publishers have been falling over themselves to produce "little books" of everything else, presumably in the hope that the essential ingredient was the littleness, rather than the calmness. Although, at 5 inches by 7¼, "1089 and all that" makes a rather big little book, and its content couldn't be further from the banalities of "The little book of calm", there is something of a "little book of mathematics" about it, with its short chapters and personal narrative.

Gerd Gigerenzer is not a mathematician or statistician per se, but primarily a psychologist, working across disciplines to understand how human beings make decisions in the face of uncertainty. What he offers here is nothing less than a prescription for how to think, how to choose, and how to live, when the information on which we base our decisions is necessarily incomplete and flawed. For example - how worried should you be if you have a positive mammogram as part of a screening programme for breast cancer, or a positive HIV test despite the fact that you are in a low-risk group?

Euclid defined what later became known as the Golden Ratio thus:
A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.

Anyone who thought geometry was boring or dry should prepare to be amazed. Despite its worthy cover this book is exactly what its title says - a story - and the plot of this story involves life, death and revolutions of understanding and belief, and stars the some of the most famous names in history.